How do you convert #r = -2 csc Ө# into cartesian form?

Question

5057 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-22T23:44:40

#y = -2#

For this problem it's good to know some trigonometric identities. For example.

Remember that in polar coordinates, we write

#x = r cos(theta)#, #y = r sin(theta)#, and #r^2 = x^2 + y^2#

Since we know that #csc(theta) = 1/sin(theta)#, we can try to rewrite our polar equation.

#r = -2 csc(theta) -> r = -2 * 1/sin(theta)#

If we multiply both sides by #sin(theta)#, we can simply replace it with #y#:

#r = -2 * 1/sin(theta)#

#r sin(theta) = -2#

Thus, in cartesian form, we get

#y = -2#